/*
Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.
*/

class Solution {
public:
    int numDistinct(string S, string T) {
        int m = S.length(), n = T.length();
        vector<int> scores(n+1, 0); scores[0] = 1;
        for (int i = 1; i <= m; i++) {
            for (int j = n; j > 0; j--) {
                scores[j] += ((S[i-1] == T[j-1])?scores[j-1]:0);
            }
        }
        return scores[n];
    }
};

#if 0
http://blog.csdn.net/abcbc/article/details/8978146
class Solution {
public:
    int numDistinct(string S, string T) {
        int m = S.length(), n = T.length();
        vector<vector<int> > scores; /* (m+1)x(n+1) */
        scores.resize(m+1);
        for (int i = 0; i < scores.size(); i++) {
            scores[i].resize(n+1);
        }
        for (int i = 0; i < m+1; i++) scores[i][0] = 1;
        for (int j = 1; j < n+1; j++) scores[0][j] = 0;
        for (int i = 1; i < m+1; i++) {
            for (int j = 1; j < n+1; j++) {
                scores[i][j] = scores[i-1][j] +
                    ((S[i-1] == T[j-1])?scores[i-1][j-1]:0);
            }
        }
        return scores[m][n];
    }
};
#endif
